esus said, "Let the little children come to me, and do not hinder them, for the kingdom of heaven belongs to such as these." (Matt. 19:14)

Did this mother come to see Jesus or, as the crowd engulfed the street, was she simply forced to simply sit on the steps and wait?

It would appear from her expression and posture that Jesus was viewed as someone important. In her arms rested an infant.

Listen to what Jesus said about chidlren. 

“He called a little child and had him stand among them. And he said: "I tell you the truth, unless you change and become like little children, you will never enter the kingdom of heaven. Therefore, whoever humbles himself like this child is the greatest in the kingdom of heaven.” (Matt. 18:2-4)